The present invention is applicable for image reconstruction from radar data acquired by a synthetic aperture radar (SAR) or by a physical radar array. SAR is a well-known and well-developed technique to produce high-resolution images. A large number of imaging algorithms are operationally used in different civilian and military application domains. A common requirement for such algorithms is that of producing imagery with the highest possible resolution. It is well known that the limits of the resolution in range and cross-range are, respectively, dictated by the frequency bandwidth and the physical dimension of the radar aperture. In practice, a criterion to assess the optimality of a SAR system is to compare the achieved cross-range resolution in the imagery with the physical dimension of the radar's antenna. As an example, in strip-map SAR, the cross-range resolution cannot be finer than a half of the physical antenna aperture size. A major part of the radar imaging algorithms presently in use have been conceived for SAR systems with an optimal aperture length. To date, the interest in radar imaging systems with sub-optimal aperture lengths has been very limited. The focus of this invention is on the problem of implementing a fast and accurate imaging algorithm with a highly sub-optimal aperture length, e.g. in a radar system having an aperture length of a few meters and illuminating an image scene spanning a few square kilometers located within the far-field of the radar aperture. This scenario is quite different from those of space-borne and air-borne SAR. In particular, the imaging algorithms used with optimal aperture lengths (typically a few tens of kilometers long in case of space-borne SAR), such as the range migration and chirp-scaling algorithms, do not satisfy certain requirements encountered with a sub-optimal radar aperture. The polar format or range-Doppler algorithm was also discarded because of the geometric distortion caused by it in the imagery. This algorithm can only be used with image extents much smaller than the range to the center of the scene and, therefore, is not appropriate for all interesting scenarios. In, Averbuch et al. disclose a method for manipulating the Fourier transform in Polar coordinates, which uses as a central tool a so-called pseudo-polar FFT, where the evaluation frequencies lie in an oversampled set of nonangularly equispaced points. The pseudo-polar transform plays the role of a nearly-polar system from which conversion to polar coordinates uses processes relying only on 1D FFTs and interpolation operations.
An example application field for a sub-optimal imaging radar is that of ground-based SAR (GB-SAR), which is presently used to monitor the displacement of landslides with sub-millimeter accuracy. In the last ten years, the Joint Research Centre of the European Commission has been a pioneer of this technology and has carried out a vast number of field campaigns that have demonstrated its operational use. This activity has resulted into a massive archive of GB-SAR data with more than 300,000 sets of raw data collected in various sites. Typically, a site monitored on a permanent basis with one of our GB-SAR instruments produces a total of 35,000-40,000 sets of raw data in an entire year. A motivation of this work comes from the need to have a computationally efficient and accurate GB-SAR processing chain to cope with this huge volume of data.